PSI - Issue 2_B

Francesco Caimmi et al. / Procedia Structural Integrity 2 (2016) 166–173 Author name / Structural Integrity Procedia 00 (2016) 000–000

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were also used (Figure 2(b)). In this work pre-cracked specimens with the following dimension were used: B =8 mm, W =16 mm 1 b = 24 mm, 2 b = 40 mm, / a W =0.3 and c values equal to 6 and 3 mm were used; in this case the shorter is c , the higher the resulting mode II component.

(a)

(b)

(c)

Figure 2. Specimen used in this work. (a) SEN(B) (if 0 d  ) and MMB. (b) A4PB. (c) CENS. Finally, to measure pure Mode II toughness values, the so-called compact edge notch shear (CENS) specimen was used (see Caimmi et al. (2006) for a thorough description of the specimen); such a specimen, shown in Figure 2 (c) is basically a variation of classical edge-notch shear specimens. The PMMA specimen is glued with an acrylic adhesive to a steel jig, gray-filled in Figure 2 (c), which can be connected to a standard dynamometer. The load is applied via a pin on the top face of the right steel part, along the crack line. In this work specimens with L =35 mm and / a L =0.6 were used. The out of plane thickness B in this case was 10 mm. All the test were run under crosshead displacement control at a rate of 5 mm/min. Fracture toughness was determined for all the specimens starting from the load displacement traces and following the ISO 13586 prescriptions to determine the initiation load. The shape factors used to calculate the critical SIFs were taken from Fett (2008) for the MMB specimens, from He and Hutchinson (2000) for the A4PB specimens and by running FE simulations for the CENS specimens (see Caimmi et al. (2006) for the details). 3.2. Numerical modelling Peridynamics models of the specimens described in the previous subsections were created (Figure 3). To solve the peridynamics equations of motion (Eq.(1)) in a quasi-static setting, i.e. assuming the contribution of the inertial term to be negligible, the open source peridynamics solver Peridigm was used (Parks et al. 2012). PMMA was modelled as a linear peridynamics solid with K =3.9 GPa and G = 0.93 GPa, which were derived by the elastic modulus measured by tensile tests and by assuming a Poisson’s coefficient equal to 0.33. The horizon was assumed to be  =0.75 mm. A brittle damage model based on a critical bond stretch (Sec. 2.) was used. The value of c s was initially estimated by the formulae valid for bond-based peridynamics formulations, provided by Silling and Askari (2005), which link c s to the critical strain energy release rate IC G and the horizon. The value was then adjusted by hand fitting in order to reproduce the fracture load recorded in SEN(B) experiments with B =4 mm; c s was thus determined to be about 1.3 10 -2 . This value was then used to simulate the behavior of mixed-mode and mode II specimens. As to the discretization, if x  is the typical grid spacing between two different discretized material points, it is necessary that the mesh resolution r x    be greater than 2; values between 3 and 4 are generally chosen to balance accuracy and computational costs (Ha and Bobaru (2010)), which increase very fast with the number of neighbors in each family. In this preliminary study, a value of r equal to 3 was used almost everywhere: for example, with reference to Figure 3(a), discretization used for three point bending specimens with S =32 mm